Enumerations for Permutations by Circular Peak Sets
نویسندگان
چکیده
The circular peak set of a permutation σ is the set {σ(i) | σ(i−1) < σ(i) > σ(i+1)}. In this paper, we focus on the enumeration problems for permutations by circular peak sets. Let cpn(S) denote the number of the permutations of order n which have the circular peak set S. For the case with |S| = 0, 1, 2, we derive the explicit formulas for cpn(S). We also obtain some recurrence relations for the sequence cpn(S) and give the formula for cpn(S) in the general case.
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